Prove that the triangle formed by the points `1,(1+i)/(sqrt(2)),a n di` as vertices in the Argand diagram is isosceles.

Explanation

To prove that the triangle formed by the points \(1\), \(\frac{1+i}{\sqrt{2}}\), and \(i\) as vertices in the Argand diagram is isosceles, we will calculate the lengths of the sides of the triangle and show that at least two sides are equal.

### Step 1: Identify the vertices
The vertices of the triangle are:
- \(A = 1\) (which corresponds to the point \((1, 0)\))
- \(B = \frac{1+i}{\sqrt{2}} = \left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)
- \(C = i\) (which corresponds to the point \((0, 1)\))

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